A transition piece of the type noted above is exemplified in U.S. Pat. No. 5,414,999, the disclosure of which is incorporated by reference herein. This invention addresses perceived shortcomings in the transition piece disclosed therein. As disclosed therein, the transition piece has an inlet to receive hot gases and an outlet to discharge the gases. Moreover, the transition piece has a frame, which frames the outlet and which has three ribs surrounding and extending away from the outlet. The frame has a longer, arcuate portion, a shorter, arcuate portion, two lateral, radial portions, which are shorter than the shorter, arcuate portion, and four rounded, corner portions joining the arcuate and radial portions. Moreover, a mounting connector extends from a middle one of those ribs, away from the outlet.